Abdelhamid Hassairi

Learn More
This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic(More)
In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families (NEF's). The first property says that the cu-mulant function of any basis of the family is a solution of some Monge-Ampère equation, the second is that the variance function satisfies a differential equation, and the third is(More)
The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the(More)
In this paper, we introduce, for a multiplier χ, a notion of generalized power function x → ∆ χ (x), defined on the homogeneous cone P of a Vinberg algebra A. We then extend to A the famous Gindikin result, that is we determine the set of multipliers χ such that the map θ → ∆ χ (θ −1), defined on P * , is the Laplace transform of a positive measure R χ. We(More)
  • 1